In a word, no.
Whether just an amplifier or built-in to an active loudspeaker, the class of amplification has no bearing on the sound. An amplifier, whether Classes A, AB or D just amplifies, it puts out a bigger version of what went in.
Consequently, unless the amplifier is heroically badly designed, and that can happen to any class, the sound won't change. How the crossover is done, and what DSP is applied will make a far bigger difference than what the amplifier is.
S.